Structural Information Learning Machinery: Learning from Observing, Associating, Optimizing, Decoding, and Abstracting
This work introduces a foundational framework for learning machines, potentially impacting all of ML/AI by merging computation and information theories, though it appears incremental in its theoretical approach.
The authors propose structural information learning machines (SiLeM), a model that defines learning as an information optimization problem to eliminate uncertainty in data spaces, using an encoding tree method to maximize decoding information and interpret essential structures.
In the present paper, we propose the model of {\it structural information learning machines} (SiLeM for short), leading to a mathematical definition of learning by merging the theories of computation and information. Our model shows that the essence of learning is {\it to gain information}, that to gain information is {\it to eliminate uncertainty} embedded in a data space, and that to eliminate uncertainty of a data space can be reduced to an optimization problem, that is, an {\it information optimization problem}, which can be realized by a general {\it encoding tree method}. The principle and criterion of the structural information learning machines are maximization of {\it decoding information} from the data points observed together with the relationships among the data points, and semantical {\it interpretation} of syntactical {\it essential structure}, respectively. A SiLeM machine learns the laws or rules of nature. It observes the data points of real world, builds the {\it connections} among the observed data and constructs a {\it data space}, for which the principle is to choose the way of connections of data points so that the {\it decoding information} of the data space is maximized, finds the {\it encoding tree} of the data space that minimizes the dynamical uncertainty of the data space, in which the encoding tree is hence referred to as a {\it decoder}, due to the fact that it has already eliminated the maximum amount of uncertainty embedded in the data space, interprets the {\it semantics} of the decoder, an encoding tree, to form a {\it knowledge tree}, extracts the {\it remarkable common features} for both semantical and syntactical features of the modules decoded by a decoder to construct {\it trees of abstractions}, providing the foundations for {\it intuitive reasoning} in the learning when new data are observed.